Magnetic field effects on particle beams and their implications for dose calculation in MR guided particle therapy

Purpose To investigate and model effects of magnetic fields on proton and carbonion beams for dose calculation. Methods In a first step Monte Carlo simulations using Gate 7.1/Geant4.10.0.p03 were performed for proton and carbon ion beams in magnetic fields ranging from 0 to 3 T. Initial particle energies ranged from 60-250 MeV (protons) and 120-400 MeV/u (carbon ions), respectively. The resulting dose distributions were analyzed focusing on beam deflection, dose deformation as well as the impact of material het- erogeneities. In a second step, a numerical algorithm was developed to calculate the lateral beam position. Using the Runge-Kutta method an iterative solution of the relativistic Lorentz equation, corrected for the changing particle energy during penetration, was performed. For comparison a -index analysis was utilized, using a criteria of 2%/2 mm of the local maximum Results A tilt in the dose distribution within the Bragg peak area was observed, leading to non-negligible dose distribution changes. The magnitude was found to de-pend on the magnetic field strength as well as on the initial beam energy. Comparison of the 3 T dose distribution with non B field (nominal) dose distributions, resulted in a mean (mean value of the distribution) of 0.6, with 14.4% of the values above 1 and 1% (1% of all points have an equal or higher value) of 1.8. The presented numerical algorithm calculated the lateral beam offset with maximum errors of less than 2% with calculation times of less than five microseconds. The impact of tissue interfaces on the proton dose distributions was found to be less than 2% for a dose voxel size of 1 x 1 x 1 mm3. Conclusion Non-negligible dose deformations at the Bragg peak area were identi-fied for high initial energies and strong magnetic fields. A fast numerical algorithm based on the solution of the energy corrected relativistic Lorentz equation was able to describe the beam path, taking into account the particle energy, magnetic field and material. This article is protected by copyright. All rights reserved.